DOI: 10.24193/fpt-ro.2024.1.11

Authors: Farhang Jahangir and Kourosh Nourouzi

Abstract: We show that full Hilbert C*-modules over a commutative unital C*-algebra 𝒜 have fixed point property for nonexpansive mappings if and only if 𝒜 is finite dimensional. We also show that the same is true for every Hilbert C*-module with unit vectors over an arbitrary unital C*-algebra. In particular, a classification of full Hilbert C*-modules with unit vectors over unital C*-algebras is given via fixed point property for nonexpansive mappings.

Key Words and Phrases: Fixed point, nonexpansive mapping, Hilbert C*-module, continuous field of Hilbert spaces, unit vector.

2010 Mathematics Subject Classification: 47H10, 46C50.

Published on-line: February 1st, 2024.

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